Your mother's first cousin is your first cousin once removed.
Your mother's second cousin is your second cousin once removed.
If you are talking about your mother's first cousin once removed, you may be first cousins twice removed or second cousins, depending on the specifics.
The daughter of your mother's first cousin is your second cousin.
The daughter of your mother's second cousin is your third cousin.
Second cousins
Cousins
Your cousin's daughter is your first cousin once removed. Your daughter and your cousin's daughter would be second cousins.
They would be cousins.
Your relationship would be that of cousins.
Your nephew and your daughter are first cousins.
You are First Cousins
You are cousins
Your great uncle's kids are your parent's first cousins. His grandchildren are your second cousins.
Your daughter and your niece are first cousins Your daughter and your great grand niece are first cousins, twice removed.
Your child and your sister's daughter are first cousins. Your grand child and your sister's daughter are first cousins, once removed.
Your daughter and your niece are first cousins to each other.